Question: Simplify the following expression: $x = \dfrac{-6y^2 + 18y + 24}{y - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-6$ , so we can rewrite the expression: $ x =\dfrac{-6(y^2 - 3y - 4)}{y - 4} $ Then we factor the remaining polynomial: $y^2 {-3}y {-4} $ ${-4} + {1} = {-3}$ ${-4} \times {1} = {-4}$ $ (y {-4}) (y + {1}) $ This gives us a factored expression: $\dfrac{-6(y {-4}) (y + {1})}{y - 4}$ We can divide the numerator and denominator by $(y + 4)$ on condition that $y \neq 4$ Therefore $x = -6(y + 1); y \neq 4$